论文标题
分布式订购时间分数波方程
Distributed-order time-fractional wave equations
论文作者
论文摘要
分布式 - 级分数波方程出现在粘弹性介质中波传播的建模中。培养基的材料特征是通过分布式构成定律中的构型函数或分布来建模的。在这项工作中，我们建议对构型“函数”采取正面ra。 首先，我们对本构措施进行热力学限制，该量度易于检查，因此适用于应用。然后，我们证明，与衍生的热力学限制相结合的设置保证了分布式分数波方程的溶液的存在和唯一性。我们进一步讨论了基本解决方案的支持和规律性，并以有关波速的讨论得出结论。
Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through constitutive functions or distributions in the distributed-order constitutive law. In this work we propose to take positive Radon measures for the constitutive "functions". First, we derive a thermodynamical restriction on the constitutive measures which is easy to check, and therefore suitable for applications. Then we prove that the setting with measures in combination with the derived thermodynamical restriction guarantee existence and uniqueness of solutions for the distributed-order fractional wave equation. We further discuss the support and regularity of the fundamental solution, and conclude with a discussion on wave velocities.
